Let's say the default website is "A" after logging on.

1. In the dashboard select site "B".
2. Go to Tag Manager and do Tag Manager stuff for site "B".
3. Return to the dashboard.
   --> Site "A" is now selected in the dashboard.

When exiting tag manager it would be better if the same site that was selected in tag manager were selected when returning to the dashboard, not the default or any other site.